Details

analyze471.0ms (6.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	176×	body	128	valid
8.0ms	28×	body	1024	valid
7.0ms	30×	body	2048	valid
2.0ms	6×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify227.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_789`
14×	`*-un-lft-identity_binary64_767`
9×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806` `add-cube-cbrt_binary64_802`
6×	`times-frac_binary64_773` `associate-/l*_binary64_712` `sqrt-prod_binary64_783` `difference-of-squares_binary64_736`
5×	`pow1_binary64_828`
4×	`cancel-sign-sub-inv_binary64_733` `flip--_binary64_742` `flip3--_binary64_771`
3×	`distribute-lft-out--_binary64_719`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `diff-log_binary64_859` `div-exp_binary64_818` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series526.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
131.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune418.0ms (6.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Merged error: 6.3b

Counts

87 → 9

Compiler

Compiled 8164 to 5509 computations (32.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.7b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
10.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
22×	`times-frac_binary64_773`
21×	`*-un-lft-identity_binary64_767`
17×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
13×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
12×	`add-sqr-sqrt_binary64_789`
11×	`associate-/l*_binary64_712` `add-cube-cbrt_binary64_802`
6×	`associate-/r/_binary64_713` `add-log-exp_binary64_806`
5×	`distribute-lft-out_binary64_718` `associate-/r*_binary64_711` `pow1_binary64_828`
4×	`flip-+_binary64_741` `flip3-+_binary64_770` `div-inv_binary64_764`
3×	`sqrt-prod_binary64_783`
2×	`frac-2neg_binary64_778` `clear-num_binary64_766` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771`

Counts

4 → 102

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series954.0ms (14%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
305.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
132.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4977	3121
1	4977	3121

prune333.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	114	9	123

Merged error: 6.2b

Counts

123 → 9

Compiler

Compiled 6924 to 4518 computations (34.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_767`
15×	`add-sqr-sqrt_binary64_789`
14×	`add-cube-cbrt_binary64_802`
12×	`times-frac_binary64_773`
8×	`add-log-exp_binary64_806`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`distribute-lft-out_binary64_718` `pow1_binary64_828`
4×	`associate-/r*_binary64_711`
3×	`associate-/l*_binary64_712` `sqrt-prod_binary64_783`
2×	`associate-/r/_binary64_713` `flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series643.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
125.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5091	1969

prune112.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 6.2b

Counts

93 → 9

Compiler

Compiled 2460 to 1455 computations (40.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_767`
18×	`associate-r_binary64_707`
16×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
14×	`add-sqr-sqrt_binary64_789`
13×	`add-cube-cbrt_binary64_802`
12×	`times-frac_binary64_773`
10×	`pow1_binary64_828`
8×	`add-log-exp_binary64_806`
6×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
4×	`distribute-lft-out_binary64_718`
3×	`sqrt-prod_binary64_783` `pow-prod-down_binary64_838`
2×	`cbrt-undiv_binary64_801` `associate-/r/_binary64_713` `flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`associate-l_binary64_708` `rem-sqrt-square_binary64_780` `sub-neg_binary64_760` `-commutative_binary64_698` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `associate-r/_binary64_709` `sqrt-pow1_binary64_785` `div-inv_binary64_764`

Counts

4 → 77

Calls

4 calls:

16.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series680.0ms (10%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
120.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4879	1915
1	4879	1915

prune146.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	88	10	98

Merged error: 6.2b

Counts

98 → 10

Compiler

Compiled 2916 to 1823 computations (37.5% saved)

regimes135.0ms (2%)

Compiler: Compiled 537 to 435 computations (19% saved)

bsearch111.0ms (1.6%)

Steps

Iters	Range	Point
11	1.533617338164353e+90	3.5739920072306705e+109	6.972667102848289e+99
8	-7.009141771871467e-292	-2.349509325897326e-294	-1.8145284637786566e-293
8	-1.0322269454701605e+98	-2.7621719849249905e+94	-1.3014879836557515e+97

Iters

Range

Point

1.533617338164353e+90

3.5739920072306705e+109

6.972667102848289e+99

-7.009141771871467e-292

-2.349509325897326e-294

-1.8145284637786566e-293

-1.0322269454701605e+98

-2.7621719849249905e+94

-1.3014879836557515e+97

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	85
1	103	85

end0.0ms (0%)

sample1.5s (21.5%)

Algorithm

1×

intervals

Results

307.0ms	1206×	body	2048	valid
280.0ms	5148×	body	128	valid
140.0ms	708×	body	1024	valid
131.0ms	412×	body	4096	valid
52.0ms	358×	body	512	valid
35.0ms	679×	body	128	nan
21.0ms	399×	body	128	invalid
19.0ms	168×	body	256	valid

Compiler

Compiled 294 to 220 computations (25.2% saved)

Details

analyze471.0ms (6.9%)

sample39.0ms (0.6%)

simplify227.0ms (3.3%)

prune8.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series526.0ms (7.7%)

simplify76.0ms (1.1%)

prune418.0ms (6.2%)

localize14.0ms (0.2%)

rewrite56.0ms (0.8%)

series954.0ms (14%)

simplify73.0ms (1.1%)

prune333.0ms (4.9%)

localize15.0ms (0.2%)

rewrite33.0ms (0.5%)

series643.0ms (9.5%)

simplify68.0ms (1%)

prune112.0ms (1.6%)

localize12.0ms (0.2%)

rewrite41.0ms (0.6%)

series680.0ms (10%)

simplify91.0ms (1.3%)

prune146.0ms (2.1%)

regimes135.0ms (2%)

bsearch111.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (21.5%)

Profiling